I was at teacher’s conference (WestCAST 2015) the other week and I heard an interesting idea for how to teach percentages. After tweaking the idea for a little while, I think I am ready to share it.

A percent is a part of a hundred. The word comes from the Latin adverbial phrase *per centum* meaning *by the hundred*.^{1} Suppose we have 100 people in a room. If 40 are men and 60 are women we say 40 percent are men and 60 percent are women. We often use the symbol “%” instead of the word “percent.”

Consider the following picture of Mario:

Let’s investigate different sections of Mario and determine the percentage of each colour. To do this, we will use a sheet of paper with a 10 by 10 hole cut in it. Thus, we will only ever see 100 squares at a time. Suppose I place the paper and this is what I see.

Let’s count the number of times each colour appears:

Tan: 7

Red: 15

Blue: 39

White: 39

First, we notice that 7 + 15 + 39 + 39 = 100 which is good because there are supposed to be 100 squares! Second, it is as easy as adding a percent symbol to turn these numbers into percentages.

Tan: 7%

Red: 15%

Blue: 39%

White: 39%

I really like this activity for a number of reasons. First, it clearly communicates that percentages are proportions of a hundred. Second, each student can place the 10 by 10 hole on a different part of Mario and get a different answer. Third, if the students are interested in the concept, they can design their own pictures in Excel to create percentage activities.

As a follow up activity, we could ask the question, what is the percentage of white squares in the entire picture of Mario? How can we calculate percent when we have more than 100 squares?